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The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation

Paul, M. R. and Clark, M. T. and Cross, M. C. (2006) The stochastic dynamics of micron and nanoscale elastic cantilevers in fluid: fluctuations from dissipation. Nanotechnology, 17 (17). pp. 4502-4513. ISSN 0957-4484. doi:10.1088/0957-4484/17/17/037.

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The stochastic dynamics of micron and nanoscale cantilevers immersed in a viscous fluid are quantified. Analytical results are presented for long slender cantilevers driven by Brownian noise. The spectral density of the noise force is not assumed to be white and the frequency dependence of the noise force is determined from the fluctuation-dissipation theorem. The analytical results are shown to be useful for the micron scale cantilevers that are commonly used in atomic force microscopy. A general thermodynamic approach is developed that is valid for cantilevers of arbitrary geometry as well as for arrays of multiple cantilevers whose stochastic motion is coupled through the fluid. It is shown that the fluctuation-dissipation theorem permits the calculation of stochastic quantities via straightforward deterministic methods. The thermodynamic approach is used with deterministic finite element numerical simulations to quantify the auto-correlation and noise spectrum of cantilever fluctuations for a single micron scale cantilever and the cross-correlations and noise spectra of fluctuations for an array of two experimentally motivated nanoscale cantilevers as a function of cantilever separation. The results are used to quantify the noise reduction possible using correlated measurements with two closely spaced nanoscale cantilevers.

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Additional Information:© IOP Publishing Limited 2006. Received 28 April 2006, in final form 26 June 2006. Published 21 August 2006. Print publication: Issue 17 (14 September 2006) This research was partially supported by DARPA/MTO Simbiosys under grant F49620-02-1-0085 and an ASPIRES grant from Virginia Tech. This work was carried out in collaboration with the Caltech BioNEMS effort (ML Roukes, PI) and we gratefully acknowledge extensive interactions with this team.
Issue or Number:17
Record Number:CaltechAUTHORS:PAUnano06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4957
Deposited By: Archive Administrator
Deposited On:15 Sep 2006
Last Modified:12 Jul 2022 19:45

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